Mostly by outside view analogy with the history of the development of science. I've read a number of ancient Greek and Roman philosophers (along with a few post-modernists) arguing against the possibility of a coherent theory of physics using arguments very similar to the ones people are using against morality.

I've also read a (much larger) number of philosophers trying to shoehorn what we today call science into using the only meta-theory then available in a semi-coherent state: the meta-theory of mathematics. Thus we see philosophers, Descartes being the most famous, trying and failing to study science by starting with a set of intuitively obvious axioms and attempting to derive physical statements from them.

I think people may be making the same mistake by trying to force morality to use the same meta-theory as science, i.e., asking what experiences moral facts anticipate.

As for likely I'm not sure how likely this is, I just think its more likely then a lot of people on this thread assume.